{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Introduction to Quantitative Finance\n",
    "\n",
    "Copyright (c) 2019 Python Charmers Pty Ltd, Australia, <https://pythoncharmers.com>. All rights reserved.\n",
    "\n",
    "<img src=\"img/python_charmers_logo.png\" width=\"300\" alt=\"Python Charmers Logo\">\n",
    "\n",
    "Published under the Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0) license. See `LICENSE.md` for details.\n",
    "\n",
    "Sponsored by Tibra Global Services, <https://tibra.com>\n",
    "\n",
    "<img src=\"img/tibra_logo.png\" width=\"300\" alt=\"Tibra Logo\">\n",
    "\n",
    "\n",
    "## Module 1.6: Time Series\n",
    "\n",
    "### 1.6.4 ARMA\n",
    "\n",
    "We have seen two models for time series analysis - Moving Average processes, and Autoregressive processes.\n",
    "\n",
    "The autoregressive model for predicting the value of a variable in a time series. We use the annotation $AR(n)$ for an autoregressive model with $n$ periods.\n",
    "\n",
    "$AR(n) X_t = c + \\sum_{i=0}^n{\\beta_i X_{t-n+1}} + u_t$\n",
    "\n",
    "We can simplify in the case of an AR(1) model, that is $n=1$. This simplifies further if we also assume a zero mean (which can be done by demeaning the data beforehand) and an error term that is white noise:\n",
    "\n",
    "$AR(1) = \\beta X_{t-1}$\n",
    "\n",
    "\n",
    "An MA model is given as:\n",
    "\n",
    "$MA(p) X_t = \\mu + \\epsilon_{t} + \\sum_{i=1}^{p}\\theta_i\\epsilon_{t-i}$\n",
    "\n",
    "and specifically the MA(1) process as:\n",
    "\n",
    "$MA(1)X_t = \\epsilon_t + \\theta \\epsilon_{t-1}$\n",
    "\n",
    "\n",
    "The difference here is subtle, but critically important. For a MA model, the correlation is 0 when the time periods are different by more than 1. That is, when some effect happens that changes the value of $X_t$ (say, a sudden high impact event), it only affects the price for two time periods. After that, we are back to \"business as usual\". For an AR model, $X_t$ depends on $X_{t-1}$. This in turn depends on $X_{t-2}$, and so on. So that shock has an almost permanent (although significantly diminishing) effect on the value of $X_t$.\n",
    "\n",
    "The main difference is that MA depends on the lagged error, which is iid, while the AR model depends on the lagged value, which is not.\n",
    "\n",
    "As you might have guessed by now, ARMA is a combination of both models, and combines the predictive power of both.\n",
    "\n",
    "An $ARMA(p, q)$ model, where $p$ is the lag in the autoregressive model and $p$ is the lag in the moving-average model is given as:\n",
    "\n",
    "$X_t = c + \\epsilon_t + \\sum_{i=1}^{q}{\\beta X_{t-i}} + \\sum_{i=1}^{p}\\theta_i\\epsilon_{t-i}$\n",
    "\n",
    "(where $c$ is the bias, and would be 0 if the data was demeaned beforehand - and therefore could be set as the overall mean)\n",
    "\n",
    "As a general rule, one would choose the lowest $p$ and $q$ values that adequately describe the data, over larger values that have better predictive power.\n",
    "\n",
    "To fit an ARMA model, once $p$ and $q$ have been chosen, a least squares regression will normally work, which will minimise the error term.\n",
    "\n",
    "To choose $p$ and $q$ themselves, there are several methods. A subjective model is to use a autocorrelation function to choose a value for $p$, and then fit $q$ afterwards:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%run setup.ipy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import quandl"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from statsmodels import api as sms"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "employment = quandl.get(\"FRED/NROUST\").diff().dropna()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: xlabel='Date'>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "employment.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "pac = sms.tsa.pacf(employment)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "from statsmodels.graphics.tsaplots import plot_pacf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "c:\\Python311\\Lib\\site-packages\\statsmodels\\graphics\\tsaplots.py:348: FutureWarning: The default method 'yw' can produce PACF values outside of the [-1,1] interval. After 0.13, the default will change tounadjusted Yule-Walker ('ywm'). You can use this method now by setting method='ywm'.\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_pacf(employment, lags=np.arange(24));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A good value here might be 1 - i.e. employment moves as it did the previous month. Another good option is 12, indicating that year-on-year changes in employment are regular (which makes sense for seasonal staff)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A subjective method for choosing $q$, the lag in the MA model, is to use the full correlation function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: xlabel='Lag', ylabel='Autocorrelation'>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pd.plotting.autocorrelation_plot(employment)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "ac = sms.tsa.acf(employment,nlags=24)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x18b53bd7710>]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(ac)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here, perhaps a lower value is more indicative."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise\n",
    "\n",
    "Research the *partial autocorrelation function*, and the *autocorrelation function*. The two are different in important ways. How are they different, and what does each tell you about the data? "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The autocorrelation is the correlation of time t with time with lag n i.e. how correlated is the current day with each of previous days individually. This highlights to me how important each of these lags are individually. The partial autocorrelation is a regression of all the lags up to n, where the value is the beta of the final lag n. It controls for the intermediate lags, ie how much extra does the final lag yield above the intermediate lags. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Objective methods for choosing parameters\n",
    "\n",
    "A more objective method is to try many different values for $p$ and $q$ and select the most informative, that is, the one that explains the data best. The `statsmodels` package has a useful function for this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "from statsmodels.tsa import stattools"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "employment.index.freq = \"QS-OCT\"  # Define our frequency as \"quarters from October, start of month\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "c:\\Python311\\Lib\\site-packages\\statsmodels\\base\\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals\n",
      "  warnings.warn(\"Maximum Likelihood optimization failed to \"\n",
      "c:\\Python311\\Lib\\site-packages\\statsmodels\\base\\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals\n",
      "  warnings.warn(\"Maximum Likelihood optimization failed to \"\n",
      "c:\\Python311\\Lib\\site-packages\\statsmodels\\tsa\\statespace\\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.\n",
      "  warn('Non-stationary starting autoregressive parameters'\n",
      "c:\\Python311\\Lib\\site-packages\\statsmodels\\tsa\\statespace\\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.\n",
      "  warn('Non-invertible starting MA parameters found.'\n",
      "c:\\Python311\\Lib\\site-packages\\statsmodels\\base\\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals\n",
      "  warnings.warn(\"Maximum Likelihood optimization failed to \"\n",
      "c:\\Python311\\Lib\\site-packages\\statsmodels\\base\\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals\n",
      "  warnings.warn(\"Maximum Likelihood optimization failed to \"\n"
     ]
    }
   ],
   "source": [
    "statistics = stattools.arma_order_select_ic(employment)  # May take a few minutes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-1473.728271</td>\n",
       "      <td>-1739.463070</td>\n",
       "      <td>-1876.189397</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-2041.330410</td>\n",
       "      <td>-2041.665546</td>\n",
       "      <td>-2043.957741</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-2043.945388</td>\n",
       "      <td>-2024.094170</td>\n",
       "      <td>-2055.411497</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-2042.386581</td>\n",
       "      <td>-2034.084434</td>\n",
       "      <td>-2056.249903</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-2045.349240</td>\n",
       "      <td>-2035.966562</td>\n",
       "      <td>-2026.223359</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             0            1            2\n",
       "0 -1473.728271 -1739.463070 -1876.189397\n",
       "1 -2041.330410 -2041.665546 -2043.957741\n",
       "2 -2043.945388 -2024.094170 -2055.411497\n",
       "3 -2042.386581 -2034.084434 -2056.249903\n",
       "4 -2045.349240 -2035.966562 -2026.223359"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "statistics['bic']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise\n",
    "\n",
    "Review the documentation for this function and identify:\n",
    "\n",
    "1. What does 'bic' stand for?\n",
    "2. What other options can be selected?\n",
    "3. What the columns specify (i.e. $p$ or $q$)?\n",
    "4. What does the index represent?\n",
    "5. Which value should we select? Are higher or lower values better?\n",
    "6. Find a shortcut parameter that gives us this value without the need to compute it?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*For solutions, see `solutions/bic_results.py`*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ARMA\n",
    "\n",
    "Once you have your parameters, fit an ARMA model using them, and review the results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "p = 3\n",
    "q = 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "from statsmodels import api as sms\n",
    "model = sms.tsa.ARIMA(employment, order=(0, p, q))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "c:\\Python311\\Lib\\site-packages\\statsmodels\\base\\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals\n",
      "  warnings.warn(\"Maximum Likelihood optimization failed to \"\n"
     ]
    }
   ],
   "source": [
    "results = model.fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>SARIMAX Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>         <td>Value</td>      <th>  No. Observations:  </th>    <td>331</td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>            <td>ARIMA(0, 3, 2)</td>  <th>  Log Likelihood     </th> <td>1001.854</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>            <td>Thu, 08 Feb 2024</td> <th>  AIC                </th> <td>-1997.708</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                <td>18:35:06</td>     <th>  BIC                </th> <td>-1986.329</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Sample:</th>             <td>04-01-1949</td>    <th>  HQIC               </th> <td>-1993.168</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th></th>                   <td>- 10-01-2031</td>   <th>                     </th>     <td> </td>    \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>        <td>opg</td>       <th>                     </th>     <td> </td>    \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "     <td></td>       <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ma.L1</th>  <td>   -1.9941</td> <td>    0.134</td> <td>  -14.907</td> <td> 0.000</td> <td>   -2.256</td> <td>   -1.732</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ma.L2</th>  <td>    0.9943</td> <td>    0.131</td> <td>    7.591</td> <td> 0.000</td> <td>    0.738</td> <td>    1.251</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>sigma2</th> <td>    0.0001</td> <td>  1.9e-05</td> <td>    6.546</td> <td> 0.000</td> <td> 8.71e-05</td> <td>    0.000</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Ljung-Box (L1) (Q):</th>      <td>12.73</td>  <th>  Jarque-Bera (JB):  </th> <td>25826.73</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Q):</th>                 <td>0.00</td>   <th>  Prob(JB):          </th>   <td>0.00</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Heteroskedasticity (H):</th> <td>3062.37</td> <th>  Skew:              </th>   <td>-2.17</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(H) (two-sided):</th>     <td>0.00</td>   <th>  Kurtosis:          </th>   <td>46.25</td> \n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Covariance matrix calculated using the outer product of gradients (complex-step)."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                               SARIMAX Results                                \n",
       "==============================================================================\n",
       "Dep. Variable:                  Value   No. Observations:                  331\n",
       "Model:                 ARIMA(0, 3, 2)   Log Likelihood                1001.854\n",
       "Date:                Thu, 08 Feb 2024   AIC                          -1997.708\n",
       "Time:                        18:35:06   BIC                          -1986.329\n",
       "Sample:                    04-01-1949   HQIC                         -1993.168\n",
       "                         - 10-01-2031                                         \n",
       "Covariance Type:                  opg                                         \n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "ma.L1         -1.9941      0.134    -14.907      0.000      -2.256      -1.732\n",
       "ma.L2          0.9943      0.131      7.591      0.000       0.738       1.251\n",
       "sigma2         0.0001    1.9e-05      6.546      0.000    8.71e-05       0.000\n",
       "===================================================================================\n",
       "Ljung-Box (L1) (Q):                  12.73   Jarque-Bera (JB):             25826.73\n",
       "Prob(Q):                              0.00   Prob(JB):                         0.00\n",
       "Heteroskedasticity (H):            3062.37   Skew:                            -2.17\n",
       "Prob(H) (two-sided):                  0.00   Kurtosis:                        46.25\n",
       "===================================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Covariance matrix calculated using the outer product of gradients (complex-step).\n",
       "\"\"\""
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_pred = results.predict()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x18b571d2250>]"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(y_pred, 'g-')\n",
    "plt.plot(employment)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Extended exercise Overfitting\n",
    "\n",
    "Don't get too excited by that graph - our model didn't predict the wild swings in unemployment (or the underlying factor of the global financial crisis). Instead, our model has been fit *to the data*, and the data included that anomaly.\n",
    "\n",
    "This is an effect known as *overfitting* - where the model fits the data, but doesn't learn about underlying trends.\n",
    "\n",
    "To counter this, we split our data into two sets - a training set and a testing set. For time series data, we want to be predicting *into the future*, so we train on the first m% of the data, and evaluate on the rest.\n",
    "\n",
    "Split the data into two groups \"Everything up to 2000\" and \"Everything else\". Train the ARMA model on the training set (the earlier data) and evaluate it on the testing data (the later data). How good does the model do?\n",
    "\n",
    "Investigate the results further. If we *ignore* the impact of the global financial crisis (as a one-off event that can't easily be modelled with the data on hand), does it do well on the years 2000-2005, and 2012-2019?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*For solutions, see `solutions/overfitting_arma.py`*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "# This next cell runs the solution file, in place, as if I copied the contents into this cell.\n",
    "# Useful for removing large bits of code from your nice looking notebooks"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "c:\\Python311\\Lib\\site-packages\\statsmodels\\tsa\\statespace\\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.\n",
      "  warn('Non-invertible starting MA parameters found.'\n",
      "c:\\Python311\\Lib\\site-packages\\statsmodels\\tsa\\statespace\\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.\n",
      "  warn('Non-stationary starting autoregressive parameters'\n",
      "c:\\Python311\\Lib\\site-packages\\statsmodels\\base\\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals\n",
      "  warnings.warn(\"Maximum Likelihood optimization failed to \"\n",
      "c:\\Python311\\Lib\\site-packages\\statsmodels\\base\\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals\n",
      "  warnings.warn(\"Maximum Likelihood optimization failed to \"\n",
      "c:\\Python311\\Lib\\site-packages\\statsmodels\\base\\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals\n",
      "  warnings.warn(\"Maximum Likelihood optimization failed to \"\n",
      "c:\\Python311\\Lib\\site-packages\\statsmodels\\base\\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals\n",
      "  warnings.warn(\"Maximum Likelihood optimization failed to \"\n",
      "c:\\Python311\\Lib\\site-packages\\statsmodels\\base\\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals\n",
      "  warnings.warn(\"Maximum Likelihood optimization failed to \"\n",
      "c:\\Python311\\Lib\\site-packages\\statsmodels\\base\\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals\n",
      "  warnings.warn(\"Maximum Likelihood optimization failed to \"\n",
      "c:\\Python311\\Lib\\site-packages\\statsmodels\\base\\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals\n",
      "  warnings.warn(\"Maximum Likelihood optimization failed to \"\n"
     ]
    },
    {
     "ename": "AttributeError",
     "evalue": "module 'statsmodels.tsa.api' has no attribute 'ARMA'",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
      "File \u001b[1;32m~\\Documents\\Prework\\Python\\QuantFinance\\notebooks\\solutions\\overfitting_arma.py:11\u001b[0m\n\u001b[0;32m      7\u001b[0m statistics[\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mbic\u001b[39m\u001b[38;5;124m'\u001b[39m]\n\u001b[0;32m      9\u001b[0m statistics\u001b[38;5;241m.\u001b[39mbic_min_order\n\u001b[1;32m---> 11\u001b[0m model \u001b[38;5;241m=\u001b[39m \u001b[43msms\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mtsa\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mARMA\u001b[49m(training, order\u001b[38;5;241m=\u001b[39m(p, q))\n\u001b[0;32m     13\u001b[0m results \u001b[38;5;241m=\u001b[39m model\u001b[38;5;241m.\u001b[39mfit()\n\u001b[0;32m     15\u001b[0m results\u001b[38;5;241m.\u001b[39msummary()\n",
      "\u001b[1;31mAttributeError\u001b[0m: module 'statsmodels.tsa.api' has no attribute 'ARMA'"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%run -i solutions/overfitting_arma.py"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Reviewing the residuals (errors)\n",
    "\n",
    "After fitting any model, it is worth checking the errors made by the models, ensuring there are no patterns. In many cases, your mean error will be 0, but this doesn't tell you much about the error.\n",
    "\n",
    "To highlight this, let's look at the residuals of our model. If you haven't completed the above exercise, load the solution from the file first, run it in this notebook and then continue below\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "operands could not be broadcast together with shapes (204,) (331,) ",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "Cell \u001b[1;32mIn[32], line 1\u001b[0m\n\u001b[1;32m----> 1\u001b[0m train_residuals \u001b[38;5;241m=\u001b[39m \u001b[43mtraining\u001b[49m\u001b[43m[\u001b[49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43mValue\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m]\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mvalues\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m-\u001b[39;49m\u001b[43m \u001b[49m\u001b[43mresults\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mpredict\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mvalues\u001b[49m\n\u001b[0;32m      2\u001b[0m plt\u001b[38;5;241m.\u001b[39mplot(train_residuals);\n",
      "\u001b[1;31mValueError\u001b[0m: operands could not be broadcast together with shapes (204,) (331,) "
     ]
    }
   ],
   "source": [
    "train_residuals = training['Value'].values - results.predict().values\n",
    "plt.plot(train_residuals);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note there is no real pattern here, indicative that it is white noise. This is the goal for our modelling - we want a model that predicts the data well, and with no pattern in the residuals. \n",
    "\n",
    "If there was a pattern, then we would need to work out a way to model that too.\n",
    "\n",
    "To see an example, if we analyse the residuals of the testing dataset, we can see a clear pattern exist (note: the pattern doesn't have to be regularly repeating). There is something going on with this data, and we would need to work it out in our analysis."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "test_residuals = testing['Value'].values - y_pred.values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(test_residuals);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise\n",
    "\n",
    "Perform a formal analysis to identity if the residuals are white noise in both the training and testing case."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
